College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 447: 75



Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \log_2(\log_2 x)=1 ,$ change to exponential form. Then do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to \begin{array}{l}\require{cancel} \log_2 x=2^1 \\\\ \log_2 x=2 .\end{array} Converting to exponential form again, the equation above is equivalent to \begin{array}{l}\require{cancel} x=2^2 \\\\ x=4 .\end{array} Upon checking, $ x=4 $ satisfies the original equation.
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